A standard interpretation of this text is that when a prophet looks forward, even in sometimes thinking of the new earth, he stops short and thinks of the millennial kingdom. If you think of the millennium as a literal thousand years at the end of the old earth, that would mean it's still under the curse even though Christ is on the throne. That would explain why death still happens even though the world is a far better place. It's still not perfect. We know there is still sin because there is rebellion at the end of the millennial kingdom and destruction of the rebels as mentioned in Rev. 20.
Some reformed theologians, including Anthony Hoekema in his book The Bible and the Future, believe the language is figurative and should be thought of as saying "If someone died at 100 they would be thought a mere youth, and if they failed to reach a 100 they would be considered accursed." In other words it's not saying they actually will die, but life is so long, eternally long now, that death at any age would be unthinkable.
I am not satisfied with the second explanation, and not completely happy with the first either, but those are the standard ways of attempting to understand that portion of Isaiah 65.